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MAT 540 Week 7 Homework Chapter 3

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1. Southern Sporting Good Company makes basketballs and footballs. Each product is produced from two resources rubber and leather. Each basketball produced results in a profit of $11 and each football earns $15 in profit. The resource requirements for each product and the total resources available are as follows:

Product Resource Requirements per Unit

Rubber (lb.) Leather (ft2)

Basketball 2.8 3.7

Football 1.5 5.2

Total resources available 600 900

a. Find the optimal solution.

b. What would be the effect on the optimal solution if the profit for the basketball changed from $11 to $12?

c. What would be the effect on optimal solution if 400 additional pounds of rubber could be obtained? What would be the effect if 600 additional square feet of leather could be obtained?

2. A company produces two products, A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows:

Product Resource Requirements per Unit

Line 1 Line 2

A 11 5

B 6 9

Total Hours 65 40

a. Formulate a linear programming model to determine the optimal product mix that will maximize profit.

b. What are the sensitivity ranges for the objective function coefficients?

c. Determine the shadow prices for additional hours of production time on line 1 and line 2 and indicate whether the company would prefer additional line 1 or line 2 hours.

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